Horses playground

The horse fence is a rectangular trapezoid with an area of 400 m². The base lengths should be 31 m and 19 m. If the boards are stacked in 5 rows, how many meters of fence will they need?

Final Answer:

x =  430 m

Step-by-step explanation:

$$\begin{gathered} S=400{\text{m}}^2 \\ a=31\text{m} \\ c=19\text{m} \\ n=5 \\ S=\frac{a+c}{2}\cdot d \\ d=\frac{2\cdot S}{a+c}=\frac{2\cdot 400}{31+19}=16\text{m} \\ b=\sqrt{d^2+(a-c{)}^2}=\sqrt{16^2+(31-19{)}^2}=20\text{m} \\ o=a+b+c+d=31+20+19+16=86\text{m} \\ x=n\cdot o=5\cdot 86=430\text{m} \end{gathered}$$

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